WASHINGTON — Even with one of the largest hurdles to an immigration overhaul overcome, optimistic lawmakers on Sunday cautioned they had not finished work on a bill that would provide a path to citizenship for 11 million illegal immigrants.

The AFL-CIO and the pro-business U.S. Chamber of Commerce reached a deal late Friday that would allow tens of thousands of low-skill workers into the country to fill jobs in construction, restaurants and hotels. Yet despite the unusual agreement between the two powerful lobbying groups, lawmakers from both parties conceded that the negotiations were not finished.

“With the agreement between business and labor, every major policy issue has been resolved,” said Sen. Chuck Schumer, the New York Democrat who brokered the labor-business deal.

But it hasn’t taken the form of a bill and the eight senators searching for a compromise haven’t met about the potential breakthrough.

“We haven’t signed off,” said Sen. Lindsey Graham, R-S.C.

“There are a few details yet. But conceptually, we have an agreement between business and labor, between ourselves that has to be drafted,” he added.

Yet just before lawmakers began appearing on Sunday shows, Sen. Marco Rubio warned he was not ready to lend his name — and political clout — to such a deal without hashing out the details.

“Reports that the bipartisan group of eight senators have agreed on a legislative proposal are premature,” said Rubio, a Florida Republican who is among the lawmakers working on legislation.

Rubio, a Cuban-American who is weighing a presidential bid in 2016, is a leading figure inside his party. Lawmakers will be closely watching any deal for his approval and his skepticism about the process did little to encourage optimism.

Rubio, who is the group’s emissary to conservatives, called the agreement “a starting point” but said 92 senators from 43 states haven’t yet been involved in the process.

The detente between the nation’s leading labor federation and the powerful business lobbying group still needs senators’ approval, including a nod from Sen. John McCain, the Arizona Republican whose previous efforts came up short.

“I think we’re on track. . But as Sen. Rubio correctly says, we have said we will not come to final agreement till we look at all of the legislative language and he’s correctly pointing out that that language hasn’t been fully drafted,” Schumer said.

Sen. Jeff Flake, R-Ariz., also noted the significance of the truce between labor and business but added that this wasn’t yet complete.

“That doesn’t mean we’ve crossed every ‘i’ or dotted every ‘t,’ or vice versa,” said Flake, who is among the eight lawmakers working on the deal.

Schumer negotiated the deal between AFL-CIO president Richard Trumka and Chamber of Commerce head Tom Donohue during a late-Friday phone call. Under the compromise, the government would create a new “W” visa for low-skill workers who would earn wages paid to Americans or the prevailing wages for the industry they’re working in, whichever is higher. The Labor Department would determine prevailing wage based on customary rates in specific localities, so that it would vary from city to city.

The proposed measure would secure the border, crack down on employers, improve legal immigration and create a 13-year pathway to citizenship for the millions of illegal immigrants already here.

It’s a major second-term priority of President Barack Obama’s and would usher in the most dramatic changes to the faltering U.S. immigration system in more than two decades.

“This is a legacy item for him. There is no doubt in my mind that he wants to pass comprehensive immigration reform,” said David Axelrod, a longtime political confidant of Obama.

During the last week, an immigration deal seemed doomed. But the breakthrough late Friday restarted the talks.

Ultimately the new “W” visa program would be capped at 200,000 workers a year, but the number of visas would fluctuate, depending on unemployment rates, job openings, employer demand and data collected by a new federal bureau being pushed by labor groups as an objective monitor of the market, according to an official involved with the talks who also spoke on condition of anonymity ahead of a formal announcement.

A “safety valve” would allow employers to exceed the cap, the official said, if they could show need and pay premium wages, but any additional workers brought in would be subtracted from the next year’s cap.

The workers could move from employer to employer and would be able to petition for permanent residency and ultimately seek U.S. citizenship. Neither is possible for temporary workers now.

“As to the 11 million (illegal immigrants), they’ll have a pathway to citizenship, but it will be earned, it will be long, and it will be hard, and I think it is fair,” Graham said.

The new program would fill needs employers say they have that are not currently met by U.S. immigration programs. Most industries don’t have a good way to hire a steady supply of foreign workers because there’s one temporary visa program for low-wage nonagricultural workers but it’s capped at 66,000 visas per year and is only supposed to be used for seasonal or temporary jobs.

Separately, the new immigration bill also is expected to offer many more visas for high-tech workers, new visas for agriculture workers, and provisions allowing some agriculture workers already in the U.S. a speedier path to citizenship than that provided to other illegal immigrants, in an effort to create a stable agricultural workforce.

Schumer, Flake and Axelrod appeared on NBC’s “Meet the Press.” Graham was interviewed on CNN’s “State of the Union.”